Gas analysis based on field-dependent ion mobility is a powerful tool in a number of applications of a primary importance, e.g. public protection against terrorism as well as protection of military staff. This is because differential ion mobility spectrometers are capable of detecting traces of explosives and poison agents present in ambient air. Another possible application of such spectrometers is remote detection of illegal drugs.
Recently, new applications of broad industrial and public interest have emerged from scientific developments, e.g. in medicine for the purposes of fast non-invasive diagnostics, in food industry for early detection of food spoilage, as well as for testing of status of production processes in many industrial branches. Further, security and health of people in their everyday life may be improved by air control in enterprises, in living rooms, in cars, in streets with heavy traffic and so on. Such public applications necessitate millions of individual spectrometers and can only become realistic if such devices can be manufactured at low costs. An important step was taken with the development of micro-machined differential mobility spectrometers (“A MEMS fabricated FAIMS device”, B. Boyle, Contribution at the Conference ISIMS 2007. Mikkeli, Finland; 2007, see also http://www.owlstonenanotech.com).
The parameters of differential mobility spectrometers, e.g. their dimensions, operating voltages, operating frequencies are restricted by several conditions imposed by the filtering principle used. In addition, there are technical requirements (e.g. the miniaturization) that limit the freedom to choose the values of these parameters. This will hereinafter be elaborated in more detail.
The phenomenon of field-dependent ion mobilities was described by Mason and McDaniel in “The Mobility and Diffusion of Ions in Gases” (Wiley, New York; 1973). In the early 1980s, it was Gorshkov, who was the first to disclose a method making use of this differential mobility for spectrometry (see SU 966583), and later, in the 1990s, Buryakov et al. who presented practical implementations of the Differential Mobility Spectrometry (DMS) technique (see Soviet Technical Physics Letters 1991, vol. 17, no. 6, p. 446-447, SU 1412447, RU 2150157). Further developments of the technique were made, for instance, by Guevremont (see WO 2001/69219 and US 2005/161597 A1) and Miller (US 2005/051719 A1).
It should be borne in mind that in the literature several terms and abbreviations are used to refer to this method, e.g. Field Asymmetric Ion Mobility Spectrometry (FAIMS), Ion Mobility Increment Spectrometry (IMIS), Ion Non-Linear Drift Spectrometry, Ion Drift Spectrometry, High-Fields Asymmetric Waveform Ion Mobility Spectrometry, Field Asymmetric Ion Mobility Spectrometry, Radio-Frequency-Based Ion-Mobility Analysis, Radio Frequency Ion Mobility Spectrometry (RF-IMS) and Field Ion Spectrometry. Herein, we will use the term “Differential Mobility Spectrometry” and its abbreviation “DMS”.
A DMS device typically comprises an ionization chamber, a separation region (also referred to as “filter” or “filter chamber”) and an analysis (or detection) chamber arranged in series. According to the inventions disclosed in the publications referenced above, the carrier gas (typically, but not limited to, ambient air at atmospheric pressure) containing some additives in the gaseous state (hereafter referred to as “analytes”) is delivered into the ionization chamber by a gas flow. In the ionization chamber, the analytes are ionized and the mixture of ions and carrier gas is further delivered into the separation region by the gas flow. The separation region contains at least two electrodes (referred to as the “separation electrodes”) disposed in such a way that the gas flow carries the ions through the space between these electrodes. A high-frequency electric voltage is applied to the separation electrodes in such a way that the resulting electric field forces the ions to move transversely to the direction of the gas flow. This transversal motion is superimposed on the initial motion through the separation region caused by the gas flow. The voltage across the separation electrodes, denoted Us, is referred to herein as “separating voltage”, while the corresponding electric field, denoted Es, is referred to as the “separating” or “transversal” field. The voltage is chosen “asymmetrically”. That is, each period of the voltage consists of at least two pulses of opposite polarity; the pulses are said to have “forward” or “backward” polarities, respectively. The at least one forward pulse is chosen to be stronger (to have higher amplitude) than the at least one backward pulse, but the duration of the forward pulse(s) is chosen to be shorter than that of the backward pulse(s), so that for the electric field the equality ∫0TsEs(t)dt=0 is valid. Here, Es(t) is the transversal electric field strength, Ts is the period of its temporal variation and t is time. In general, the velocity (V) of the ions in the carrier gas subjected to an electric field E is expressed as V=KE, where K is the mobility, expressed as K=K0[1+α(E)]. Here, K0 is the ion mobility in a small electric field, while the factor α=α(E) (referred to as the “mobility increment”) accounts for the dependence of the mobility upon the electric field and represents in general a non-linear function of E2. Due to the time-dependency imposed on the transversal electric field, the average velocity gained by the ion during a period of the field is V=K0Ts−1∫0Tsα[ES(t)]×Es(t)dt. In the general case, V is non-zero and essentially depends upon the mobility increment. Thus, the applied transversal electric field results in the ions of the analytes moving towards one of the separating electrodes. As soon as they hit the electrodes, the ions reconstitute. The above publications teach that the high-frequency transversal field can be supplemented by a slowly varying component, Ec(t), (referred to as the “compensating field”) so that the transversal field has the form E(t)=Es(t)−Ec. Slowly scanning the parameter Ec reveals some values of Ec, at which a certain sort of analytes has zero average transversal velocity increment during a period of the transversal electric field: V≈∫0Tsα[Es(t)−Ec]×Es(t)dt−Ec∫0Tsα[Es(t)−Ec]dt=0. Those ions for which this relation is valid in average do not move, again in average, towards one of the separating electrodes. As a consequence, they pass through the separation region and enter the analysis chamber.
In conventional macroscopic gas-flow-driven DMS devices, the analysis chamber contains at least two electrodes connected to a measuring device through an amplifier. This enables one to register small ionic currents as the ions, which have passed through the separation region, hit one of these electrodes. Thus, the described set up enables one to register a current signal, J, as the function of the compensating electric field, Ec(t). Plotting the current signal J against Ec(t) reveals a characteristic set of peaks. The peak maxima are located at those Ec values at which (at least) one species of analytes passes through the filter. At least some of the peaks are separated from one another. Such J=J(Ec) dependence is referred to as a DMS spectrum. The DMS spectrum enables one to identify the analytes based on the differences in their mobility increments. This is the main distinction of the DMS method with respect to other gas analysis methods, such as e.g. Ion Mobility Spectrometry, Aspiration Ion Mobility Spectrometry and the Time-of-Flight Mass Spectrometry, which rely upon the mobility K0 itself (instead of its increment) to distinguish between different species of analytes. Ideally, each of the peaks of a DMS spectrum corresponds to one and only one analyte species. In practice, however, several analytes may have similar mobility increments and thus give rise to overlapping or superimposed peaks. In certain cases, peaks caused by different analytes may even be indistinguishable from one another. The reasons for this are discussed in details below.
In the patent documents and scientific papers cited above, the carrier gas charged with analytes is delivered into the device by a gas flow (provided, for instance, with a mechanical pump). In contrast to that, patent application WO 2001/035441 (Miller and Zahn) teaches to use an electric field for delivering the ions into the separation region.
The DMS filters disclosed in the contributions cited above are all of macroscopic size. Typically, they have a length of about 10 cm and a lateral dimension of a few centimeters. Patent applications WO 2007/034239 (Alonso et. al.), WO 2006/046077, WO 2006/013396 and WO 2007041551 (Boyle et. al.) disclose micro-machined DMS, in which the analyte ions are caused to drift by an electric field (longitudinal or “drive” field) oriented in direction of the gas flow and generated by a special pair of deviating electrodes. These patent applications also disclose methods of fabrication of such devices. The microscopic (sub-millimeter) size of the device is favorable, since it enables one to apply considerably smaller voltage across the separating electrodes and at the same time keep the high value of the electric field strength that is intrinsically required for DMS. This is achieved due to a strong reduction of the inter-electrode distance of the device. Further, the sub-millimeter length (i.e. the device dimension along the direction of the drift of ions) enables one to apply a relatively small voltage also in this direction.
The above-mentioned patent applications disclose devices operating with a static (that is, time-independent) longitudinal electric field. WO 2006/013396 and WO 2007/034239 also mention that the longitudinal electric field is preferably a static electric field but a time-varying drive field can be employed. The patents however, give no details on possible variations of the longitudinal electric field.
One aspect of the present invention relates to light-induced ionization of analytes. Therefore, publications related to this subject are briefly reviewed below.
At present, in about 90% of the cases, ionization in DMS devices is provided by β-radioactive sources (such as 63Ni) due to low and easy service requirements, low price and high stability of such sources. Application of β-radioactive components does not usually create a major concern in military or police applications. Mass market introduction of such β-source-based devices is, however, hindered by strict law requirements on the one hand and public prejudice against any sort of radioactivity on the other hand.
A further well established method of ionization uses the so-called electro-spray effect. Due to its intrinsic properties this method leads to a fast contamination of the devices and may be mortal for micro-devices.
The third main option for ionizing analytes is UV-light ionization. A number of aspects of UV ionization in DMS applications have already been disclosed in the past. In patent application WO 01/69219, Guevremont et al. disclosed the idea of a laser-based ionization source combined with the DMS device. The main idea of the document is to use the so-called matrix-assisted laser decomposition ionization together with DMS. In matrix-assisted laser decomposition ionization (MALDI), the solid or liquid sample is mixed with a material called a “matrix” and the combination is dried on a metal support electrode. A laser beam is directed onto this surface and ions of the analyte compound are formed. In WO 01/69219 it is proposed to use this method with a DMS of cylindrical configuration and to provide the DMS with a device able to partially remove the inner electrode on which the samples are deposited from its position, to bring it back as well as to rotate it along its axis. This document also discloses a special orifice (sample introduction port) through which the matrix/sample mixture may be applied to the inner electrode upon a partial removal of the latter. In US 2005/0161597, Guevremont et al. disclosed a set of combinations of a DMS device with one or several lasers, in which the ionization process takes place outside the DMS filter and the resulting plasma is brought into the separation region afterwards.
In the papers Borsdorf H, et al., Analytica Chimica Acta 575, 76 (2006) and Nazarov E. G., et. al. Analytical Chemistry 78, 4553 (2006), the application of krypton discharge lamps with DMS for photoionization of hydrocarbons has been described.
In addition to papers and patent documents disclosing the use of optical ionization tools for the DMS applications, a number of publications disclosed the use of UV-light ionization along with other ion-separating devices such as the Ion Mobility Spectrometer, the Time-of-Flight Mass Spectrometer etc. Those skilled in the art readily understand that normally the means applicable to those devices can be also used with DMS.
U.S. Pat. No. 4,398,152 to Leveson discloses a construction of a gas lamp in which plasma is generated by the radiofrequency AC voltage. The UV light from the lamp is intended to ionize gases in ion mobility spectrometers. Patent application WO 93/22033 discloses a construction of an Ion Mobility Spectrometer with a flash lamp as the ionization source. In this case, the flash lamp irradiates the mixture of air and analyte within the Ion Mobility Spectrometer, which results in ionization of the mixture. The resulting plasma is then delivered into the filter region. U.S. Pat. No. 5,968,837 to Adler et al. discloses to enhance photoionization by addition of dopants. U.S. Pat. No. 5,541,519 to Stearns and Wentworth discloses the combination of a flash lamp and an Ion Mobility Spectrometer. The gas to be analyzed is mixed with a rare gas in the drift chamber of the Ion Mobility Spectrometer and is subjected to a high voltage from the discharge electrodes. The following discharge causes UV irradiation ionizing the analyte gas. In U.S. Pat. No. 5,808,299 to Syage, photoionization has been proposed as a method of ionization of gases analyzed by a Mass-Spectrometer, while in EP 1 726 946 and US 2005/138594 of the same author, a combination of a discharge ionization device with a photoionization device has been proposed for increasing the sensitivity of an Ion Mobility Spectrometer. In U.S. Pat. No. 5,338,931 to G. E. Spangler and J. E. Roehl, flash lamp-based ionization for Ion Mobility Spectrometer has been disclosed. A gas sample is introduced via a carrier gas into a ionization chamber, which is part of the spectrometer cell. Ionizable molecules contained in the injected gas sample are ionized by ultraviolet light emitted from a flash lamp. In WO 2001/019501 to W. Yang and P. C. His, a photoionization device for Ion Mobility Spectrometry has been proposed, which includes either multiple UV lamps, each having a specific energy level for discriminating between potential constituents of the gas sample, or a single multiple-energy level UV lamp (does not exist yet) with different light bandwidth window zones and a zone selector.
UV photoionization was also proposed for application in time-of-flight mass spectrometer. In this context, it was shown that the use of an adsorbing surface may increase the number of the ionized molecules over three orders of magnitude (Millard JR, et. al., J. Phys. Chem. 91, 4323 (1987); WO 2001/019501 A1).
In WO 2006/013396 to Boyle et. al. it is mentioned that UV ionization sources may be used together with micro-machined DMS devices. No details of their use, however, have been disclosed.
Finally, an ionization device for Ion Mobility Spectroscopy based on X-rays has been recently reported by Heller, W. et al. in “Ion mobility spectrometry with X-ray tubes as ionization device”, Contribution at the International Symposium on Ion Mobility Spectrometry ISIMS 2007, Mikkeli, Finland; Jul. 22-27, 2007.
The nature of the DMS method imposes certain limitations on construction of DMS devices. For example, the distance between the separating electrodes (hereinafter referred to as distance d) cannot be chosen arbitrarily. First, the transversal electric field strength must reach a certain value in order to make the field-dependence of the mobility increment a measurable effect. From typical results found in literature (I. A. Buryakov et al., IJMS 128, 143 (1993); I. A. Buryakov, Talanta 61, 369 (2003); I. A. Buryakov, ZhTF 74, 15 (2004) and I. A. Buryakov, ZhTF 72, 109 (2002); G. A. Eiceman et al., Anal. Chem. 76, 4937 (2004); N. Krylova et al., J. Phys. Chem. A107, 3648 (2003) and Krylov, E. V. et. al. IJMS 266, 76 (2007)) one can conclude that the amplitude of the electric field strength Es,req required for these purposes should be in the range 104-105 V/cm. Thus, for a given inter-electrode voltage (between the separating electrodes), the inter-electrode distance d is subject to the inequality:d≦Us/Es,req  (-1-)
Second, in the inter-electrode region of the separation region, the ions of analytes follow a zigzag course. This requires that the inter-electrode distance be much larger than the amplitude of the zigzag motion, which yields the condition:(K0Ust1)1/2<<d  (-2-)where t1 is the duration of the forward phase of the period. Conditions (-1-) and (-2-) yield:Us>K0t1Es,req2  (-3-)
(-3-) defines a lower bound the separating voltage. In addition, due to technical requirements, the separating voltage should be as low as possible. In order to enable the use of comparably simple electronics and keep energy consumption and operational costs within reasonable limits, one may impose:Us≦Uup=100 V
This condition is not determined by any intrinsic physics of the phenomenon and can be considered as a “soft” requirement, in the sense that it may be varied, if necessary within the order of magnitude.
These limitations will now be estimated for the example of the Lonestar™ chemical detector produced by Owlstone Ltd. (http://www.owlstonenanotech.com/site.php). It will be assumed that the transversal electric field strength Et˜104 V/cm, (where the symbol “˜” means “equal by their orders of magnitude”) and that t1˜Ts, where Ts is the period of the separation field. In this example, the period Ts is 3×10−8 s (presentation at the ISIMS 2007, Mikkeli, Finland, Jul. 22-25, 2007). A typical estimate for the ion mobility of explosives is K0≈1 cm2/(V×s) (cf. I. A. Buryakov, ZhTF 72, 109 (2002) and A. Kudryavtsev et. al. IJIMS 4, 117 (2001)). Condition (-3-) then yields Us>3.8 V. If we assume that for technical reasons, there is an upper bound of 10 V, we find that the inter-electrode distance d may be selected in the range from 6 μm to 10 μm. Increasing the upper limit of the voltage makes the acceptable interval wider. For instance, with Us≈100 V one finds 20 μm<d<100 μm.
The next restriction is imposed on the period Ts of the oscillations of the separation field. It is related to the fact that for the filtering to be efficient the ions must make a lot of zigzag steps during the time Tf of their flight through the filter. If the ions are driven through the filter by a driving electric field (denoted Ed) caused by a voltage Ud, the time of flight is expressed as Tf=L2/K0Ud, where the length L is the dimension of the filter in the direction of flight. This yields the condition
                                                        L              2                                                      K                0                            ⁢                              U                d                            ⁢                              T                s                                                              ⁢        1                            (                              -                    ⁢          4          ⁢                      -                          )            
For instance, in a device with a length L=200 μm, a driving voltage of 40 V and an operating frequency Ts−1=10 MHz and assuming a typical ion mobility K0˜1 cm2/(V×s), one finds L2/(K0UdTs)˜100, which agrees with requirement (-4-).
In case of a static driving field, its strength must be smaller than the electric breakdown value Eb (˜3×104 V/cm in dry air at atmospheric pressure), and the corresponding driving voltage Ud should be below a technically required upper value Uup. This yields the conditions:Ud<EbL and Ud≦Uup  (-5-)
For a device with L=200 μm one obtains, therefore, Ud<600 V. Operating at the voltages close to this limit would bear the risk of electric breakdown but, in practice, the voltage is typically below the above-mentioned “soft” limit Uup.
A lower limit for the driving voltage Ud can be derived from device-related, practical limitations. The signal of the DMS device can be registered in different ways. For example, a mass spectrometer could be built in series with the DMS separation chamber and play the role of the detection region. However, the most simple and practical method is to register the ionic current directly in the detection region using an electrometer or comparable instrument. In conventional DMS devices, this is usually done by placing of at least one pair of electrodes into the detection region. In an electric-field-driven DMS device, one or both of the deflection electrodes may play the role of such detection electrodes and, in this case, only one detection electrode is situated inside the detection region. In both cases, the detected current caused by the analyte ions that reach the detection region can be expressed as:
                    J        =                                                            qN                an                                  (                  i                  )                                            ⁢                              K                0                            ⁢              A                        L                    ⁢                                    U              d                        .                                              (                              -                    ⁢          6          ⁢                      -                          )            
Here J is the ionic current measured in the detection circuit, q is the electric charge carried by the ions, A is the area of the cross-section of the separation chamber normal to the average ion trajectory and Nan(i) is the density (in particles per unit volume) of the analyte ions delivered to the detection electrode(s). The latter considerably differs from the density Nan of analyte molecules that enter the ionization chamber: Nan(i)=βNan. Factor β accounts for the efficiency of the ionization as well as for numerous losses of ions on their way to the detection region. It depends, therefore, upon the ionization method, the composition of the carrier gas and the geometries of the ionization and separation chambers. It may also equivocally depend upon the intensity of the electric field in the separation chamber and characteristics of the waveform, since these parameters influence the losses. According to equation (-6-), the minimal measurable value of the electric current Jmin—corresponding to the noise level of the electrometer—determines the minimal acceptable value for the driving voltage Ud(min). For the ionic current to be well distinguishable from noise, the driving voltage must provide a required signal-to-noise ratio R (e.g. at least 10). This yields the limitation:
                              U          d                ≥                  R          ×                                    LJ              min                                                      qN                an                            ⁢                              K                0                            ⁢              A              ⁢                                                          ⁢              β                                                          (                              -                    ⁢          7          ⁢                      -                          )            
Assuming, as an example, that the required signal-to-noise ratio is R=10, β˜0.001, L=200 mm, there are about 50 filter channels disposed in parallel having each the lateral dimensions of 100 μm×400 μm, the noise level is Jmin˜10−2 pA, Nan˜106 cm−3, K0˜1 cm2V−1s−1 and q=1.6×10−19 C per ion, on finds Ud>100 V. The ionic current, to which this driving voltage leads according to (-6-), amounts to J˜0.1 pA, which is a small but still measurable value exceeding the noise level, Jmin. The minimal acceptable value for the driving voltage thus depends upon the design of the device and the properties of the analyte through its mobility, charge and density. In this example, a very low analyte concentration was used, which corresponds to the detection limit of ˜10−12 g/l of tetraethylamine (I. A. Buryakov, E. V. Krylov et al. Zh. Analit. Khim. 1993; 48 (1): 156-65). If the device is designed for higher analyte concentrations or/and with a better efficiency, the necessary driving voltage could be lower.
Another requirement imposed on device parameters is related to the resolution of the DMS device. The arguments given below show that a conventional device is unable to distinguish ions with mobility increment α=α(0) from ions with α=α(0)±Δα, with Δα in a certain interval. For the results provided by the device to be reliable, the inequality α(0)>Δα must be fulfilled. Furthermore, the smaller is the ratio r=Δα/α(0), the higher is the resolution of the device.
Assume that an electric field E=Es(t)−Ec(0) is applied across the separating electrodes, and for a certain compensating field Ec(0), the ions possessing the mobility increment α=α(0) are not deviated to the separating electrodes, i.e. pass through the filter and are detected. Ions with α=α(0)(E)+Δα(E) (different from α(0)), however, move towards the one of the separating electrodes with the average velocity V≈K0Δα[E(t)]×E(t)≠0 and will eventually reach that electrode, provided that Δα[Es(t)]×Es(t)K0Tf≧d, where the time of flight Tf is defined as Tf=L/Vd in the general case or Tf=L2/K0Ud in case the ion flow is generated by a driving electric field. Here Vd and Ud are the longitudinal velocity and the driving voltage across the deviating electrodes, respectively. Ions with α≠α(0), but Δα[Es(t)]×Es(t)×K0Tf<d will pass through the separation region and will be registered in the analyzing chamber indistinguishable from the ions with α=α(0).
Example: Typically the mobility increment manifests itself at E/N>10 Td, where N is the air density (in particles per cm3) and unit Td (Townsend) is defined by: 1 Td=10−17 V×cm2. One usually extracts the dependence of the mobility increment, α=α(E/N), upon the reduced electric field, E/N, from experimental data in a form of a polynomial α(E/N)=α2E2/N2+α4E4/N4+ . . . , where α2 and α4 are coefficients (see, for example, Buryakov ZhTF 2004; 74(8):15-20; Buryakov Talanta 2003; 61(3):369-375 and Krylova et. al. J. Phys. Chem. A 2003; 107(19):3648-3654). If the reduced the electric field strength E/N obeys the relation E/N<<(α2/α4)1/2, the one-parametric representation α(E/N)≈α2E2/N2 accurately describes the mobility increment. The above papers (as well as other publications) report the values of α2 and α4 for various substances of interest in the range of α2≈10−6 to 10−7 Td−2 and α4≈10−10 to 10−11 Td−4, respectively. This yields a relatively broad interval of 10<E/N<100 Td, in which the mobility increment is manifested while the one-parametric representation is valid. Assuming further that the separating field is represented as follows: Es(t)=Usf(t)/d−Es, where Us is the amplitude of the voltage across the separating electrodes and f(t) is the so-called waveform, and where Ec is the compensating field. Assume that there is a sort of ions which have as mobility increment α2=α2(0) and for which the average transversal velocity is zero for a certain value of Ec. Then all the ions with α2=α2(0)+Δα2 such that K0Es3f3Δα2Tf/N2<d−K0Ust1/d will be registered in the detection chamber. Here, f3=Ts−1∫0Tsf3(t)dt and t1 is the duration of the positive pulse. One finds the condition:
                    r        =                                                            d                2                            ⁢                              N                2                            ⁢                                                U                  d                                ⁡                                  (                                                            d                      2                                        -                                                                  U                        s                                            ⁢                                              K                        0                                            ⁢                                              t                        1                                                                              )                                                                                    L                2                            ⁢                              U                s                3                            ⁢                              〈                                  f                  3                                〉                            ⁢                              α                2                                  (                  0                  )                                                              ⁢                                  1                                              (                              -                    ⁢          8          ⁢                      -                          )            which again involves the spatial dimensions of the device. If the inequality (-2-) is fulfilled, the condition (-8-) can be simplified and takes the form:
                    r        =                                                            d                4                            ⁢                              N                2                            ⁢                              U                d                                                                    L                2                            ⁢                              U                s                3                            ⁢                              〈                                  f                  3                                〉                            ⁢                              α                2                                  (                  0                  )                                                              ⁢                                  1                                              (                              -                    ⁢          9          ⁢                      -                          )            
Condition (-9-) can be useful if the parameters of the device are close to the boundary defined by (-2-). To demonstrate this condition we make use of the voltages of operation of the Owlstone device Ud=Us=40 V, its length L=200 μm, its inter-electrode distance d=100 μm. We further take the air density at normal conditions N≈1019 cm−3 and use the typical values of the parameter) α2(0)≈10−7−10−5 Td−2 (I. A. Buryakov, Talanta 61, 369 (2003) and ZhTF 72, 109 (2002), N. Krylova et al., J. Phys. Chem. A107, 3648 (2003)). In case of rectangular pulses described as f(t)=1 for 0<t≦t1 and f(t)=−Ts/(t1−Ts) for t1<t≦Ts, at a repetition rate of 10 MHz, one finds Ts=0.1 μs. Assuming t1=0.03 μs one finds f3≈0.2. This yields r≈100−10>>1. The estimate shows that such a device is unable to give reliable results. Even a 10-fold increase in filter length up to L=2 mm, yields the resolution factor close to unity r≈1−0.1, which still results in a risky regime of operation.
All parameters discussed above are important. However, the parameter r (-8-) has primary importance since its value determines whether the spectrum measured by the device has any physical sense at all. The above analysis demonstrates that there is limited freedom for varying the parameters of a micro-DMS device in order to decrease r (e.g. by variation of voltages or the inter-electrode distance d). The device length is not restricted by any condition other than (-8-) and therefore, it would be possible to increase the length, which would result in a decrease of r proportional to L−2. Considerable increase in L however, imposes problems for the micro-machining of the device.